Non-Distorted Texture Mapping for Sheared Triangulated Meshes

in: Computer Graphics (Proc. Siggraph.), pages 343--352, ACM Press, New York, NY

Abstract

This article introduces new techniques for non-distorted texture mapping on complex triangulated meshes. Texture coordinates are assigned to the vertices of the triangulation by using an iterative optimization algorithm, honoring a set of constraints minimizing the distortions. As compared to other global optimization techniques, our method allows the user to specify the surface zones where distortions should be minimized in order of preference. The modular approach described in this paper results in a highly flexible method, facilitating a customized mapping construction. For instance, it is easy to align the texture on the surface with a set of user defined isoparametric curves. Moreover, the mapping can be made continuous through cuts, allowing to parametrize in one go complex cut surfaces. It is easy to specify other constraints to be honored by the so-constructed mappings, as soon as they can be expressed by linear (or linearizable) relations. This method has been integrated successfully within a widely used C.A.D. software dedicated to geosciences. In this context, applications of the method comprise numerical computations of physical properties stored in fine grids within texture space, unfolding geological layers and generating grids that are suitable for finite element analysis. The impact of the method could be also important for 3D paint systems.

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    BibTeX Reference

    @INPROCEEDINGS{Levy98NDTM,
        author = { Levy, Bruno and Mallet, Jean-Laurent },
         title = { Non-Distorted Texture Mapping for Sheared Triangulated Meshes },
         month = { "jul" },
     booktitle = { Computer Graphics (Proc. Siggraph.) },
       chapter = { 0 },
          year = { 1998 },
         pages = { 343--352 },
     publisher = { ACM Press, New York, NY },
      abstract = { This article introduces new techniques for non-distorted texture
    mapping on complex triangulated meshes. Texture coordinates are
    assigned to the vertices of the triangulation by using an iterative optimization
    algorithm, honoring a set of constraints minimizing the
    distortions. As compared to other global optimization techniques,
    our method allows the user to specify the surface zones where distortions
    should be minimized in order of preference. The modular
    approach described in this paper results in a highly flexible method,
    facilitating a customized mapping construction. For instance, it is
    easy to align the texture on the surface with a set of user defined
    isoparametric curves. Moreover, the mapping can be made continuous
    through cuts, allowing to parametrize in one go complex
    cut surfaces. It is easy to specify other constraints to be honored
    by the so-constructed mappings, as soon as they can be expressed
    by linear (or linearizable) relations. This method has been integrated
    successfully within a widely used C.A.D. software dedicated
    to geosciences. In this context, applications of the method comprise
    numerical computations of physical properties stored in fine
    grids within texture space, unfolding geological layers and generating
    grids that are suitable for finite element analysis. The impact of
    the method could be also important for 3D paint systems. }
    }